Nuclear timescale

In contrast to the above situation, based on an average charge density (pa), one may identify another dynamical regime where the solvent electronic timescale is fast [50-52] relative to that of the solute electrons (especially, those participating in the ET process). In this case, H F remains as in Equation (3.106), treated at the Born-Oppenheimer (BO) level (i.e., separation of electronic and nuclear timescales), but HFF is replaced by an optical RF operator involving instantaneous electron coordinates [52] ... 

Following Marcus, we simplify this picture by assuming that the solvent is characterized by only two timescales, fast and slow, associated, respectively with its electronic and the nuclear response. Correspondingly, the solvent dielectric response function is represented by the total, or static, dielectric coefficient Sg and by its fast electronic component Sg (sometimes called optical response and related to the refraction index n by Sg = n ). includes, in addition to the fast electronic component, also contributions from solvent motions on slower nuclear timescales Translational, rotational, and vibrational motions. The working assumption of the... 

During the main hydrogen-core burning phase, hydrogen is converted to helium via the CNO-cycle. Consequently the star has a convective core, but this decreases in mass from 20% to 8% of the total mass during main-sequence burning. At the same time, the luminosity increases as hydrogen is depleted (see above) all on a nuclear timescale tnuc 6 x 107 years. 

We specialize now to a delta pulse EL(f) = EL8 (f) on the nuclear timescale and a parallel transition where the transition-dipole moment is parallel to the bond vector R. Then,... 

The small statistical sample leaves strong fluctuations on the timescale of the nuclear vibrations, which is a behavior typical of any detailed microscopic dynamics used as data for a statistical treatment to obtain macroscopic quantities. 

Knowledge of the underlying nuclear dynamics is essential for the classification and description of photochemical processes. For the study of complicated systems, molecular dynamics (MD) simulations are an essential tool, providing information on the channels open for decay or relaxation, the relative populations of these channels, and the timescales of system evolution. Simulations are particularly important in cases where the Bom-Oppenheimer (BO) approximation breaks down, and a system is able to evolve non-adiabatically, that is, in more than one electronic state. 

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

How well do these quantum-semiclassical methods work in describing the dynamics of non-adiabatic systems There are two sources of errors, one due to the approximations in the methods themselves, and the other due to errors in their application, for example, lack of convergence. For example, an obvious source of error in surface hopping and Ehrenfest dynamics is that coherence effects due to the phases of the nuclear wavepackets on the different surfaces are not included. This information is important for the description of short-time (few femtoseconds) quantum mechanical effects. For longer timescales, however, this loss of information should be less of a problem as dephasing washes out this information. Note that surface hopping should be run in an adiabatic representation, whereas the other methods show no preference for diabatic or adiabatic. 

In the absence of nuclear energy sources, a star contracts on a thermal timescale and radiates energy at the expense of gravitational potential energy. Since, by the Virial Theorem, the total energy... 

The assumption of weak electronic coupling may not be valid for vibrational levels near the region where the reactant and product surfaces intersect. If the extent of electronic coupling is sufficient (tens of cm ), the timescale for electron transfer for vibrational levels near the intersectional region will approach the vibrational timescale, electronic and nuclear motions are coupled, and the Born-Oppenheimer approximation is no longer valid. 

Owing to the very high intensity of SR, exposure times on nuclear plates are typically ten minutes, whereas for such a slow emulsion, exposures are of the order of days in the laboratory. This reduction in timescale is particularly important for multiple exposure topographs of deformed crystals. 

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